$$\sin(x)\cos(x) + \cos(x) = 0$$
You are asked to find all possible solutions. What I immediately did was bring over the $\cos(x)$ term and then divided across by $\cos(x)$ and then proceeded from there:
$$\sin(x)\cos(x) = -\cos(x)$$
$$\sin(x) = -1$$
Now it states in the solution which I looked at after that this is wrong. I know now after reading the solution that this will result in losing solutions in my final answer but I don't understand why. I don't think I'm breaking any rules by doing what I did above so why does it result in losing solutions. Can anyone tell me what it is I'm not understanding about this equation.
Thank you to anyone who offers help in advance!